Simplified methods of estimating daily mean stream water temperature

SUMMARY. 1. It was assumed that the average of twenty-four hourly temperature readings is the'true'daily mean. For a small stream in upper Tees-dale, northern England, estimates of the daily mean were obtained from: (a) The mean of temperature readings taken at regular but less frequent intervals than hourly (twelve, six and three times per day), (b) The daily mid-point (=¹/₂(maximum + minimum)). (c)Spot temperatures at the two times in the day when the daily temperature trace usually crosses the daily mean value. These estimates were then compared with the'true'mean.
2. The accuracy of the estimate of daily mean decreased with reduced frequency of reading but, even at only three readings per day, was always within ±0.5°C of the true value. Consolidation of the daily estimates gave estimates of monthly and annual means within ±0.1°C of the true values.
3. Nearly 96% of estimates of the daily mean based on the daily midpoint were within ±0.5°C of the true value. The estimates showed a small but statistically significant positive bias.
4. Over 80% of estimates of the daily mean based on the'first mean crossing'were within ±0.5°C of the true value and no bias could be shown.
5. Estimation of daily means from temperature at the time of the 'second mean crossing'was relatively complicated and gave less satisfactory results than did the first mean crossing.
6. The daily mid-point and the temperature at the time of the first mean crossing both gave a good general indication of daily mean temperatures. When consolidated to monthly or annual means the estimates were within ±0.25°C and ±0.10°C, respectively, of the true values.